How to Calculate Amortization

13 May 2019
by
National Bank of Canada

When you borrow money to buy a house or carry out another personal
project, amortization is a key element. Here are some basic concepts
to consider before establishing how much time it will take to pay off
your loan.

Amortization allows you to divide several payments for capital
repayment and loan interests. The amount of each payment is the same
and they are made periodically, often on a monthly or weekly basis,
for a specific period of time.

For example, if a loan is spread out over eight years, amortization
is the time it takes to reimburse the total capital and interests each
month or each week at a fixed-rate amount. It has a financial impact
on all types of loans with interest.

Although not discussed here, amortization also refers to an
accounting operation used in the preparation of business’s financial
statements and self-employed workers. It involves distributing the
cost of goods over a few years rather than registering it in full the
year of the purchase.

How to calculate amortization

Three factors are taken into account for the calculation: the amount
borrowed, the duration and the annual interest rate. You will find
many online loan calculators that, in just a few
clicks, can help you estimate the effects of amortization on a loan.

Are you curious about the logistics behind the math? Starting with
the amount of your periodic payments, you can calculate the portions
of interest and capital that you pay with each payment. Imagine that
you borrow $25,000 at 10% for 4 years at a monthly payment of $634.06.
First, convert the annual interest to a periodic rate:
10% ÷ 12 = 0.83%. Next, multiply the balance by this
rate: $ x 0.83% = $207.50 in interest (for the first month) and
$426.46 in capital ($634.06 - $207.50).

Redo the next calculation, payment by payment, each time subtracting
the capital repaid from the remaining balance. “When a loan is
amortized, the interest is always calculated from the balance,”
explains Louis-François Éthier, Director of Mortgage Products at
National Bank.

Interests and reimbursement of capital

Even if payments are equal, the portion that pays the interest on a
loan is reduced progressively as the capital balance decreases. This
is the principle of diminishing interest. If you take a look at the
amortization table, you will notice that the parts corresponding to
the capital repayment and interest payment vary from one deadline to
the next.

The amount allocated to interest is at its maximum for the first
payments and then gradually decreases. For a loan amortized over a
long period, such as a mortgage
loan, payments during the first year are used to pay interest
rather than repay capital.

For example, if you borrow $200,000 at 5.49% over 25 years to buy a
house, only around the 12th year will you begin to pay more
capital than interest. On the other hand, with a personal loan of
$20,000 at 10.15% over 5 years, the capital repayment will exceed the
interest starting with the first payment.

“It’s a simple mathematical question,” says Louis-François Éthier.
“The longer the amortization, the less the loan is repaid quickly and
the more interest there is to be paid. The shorter it is, the less you
pay for it.”

Save on a mortgage loan

A mortgage is often the most important amount
of money a person will borrow in their life. “At National Bank,
the maximum amortization period for a mortgage loan is 30 years,”
explains Louis-François Éthier. “However, most people choose to pay
off their home over 25 years.”

This 5-year difference will save you a lot of money. A mortgage loan
of $200,000 amortized over 25 years rather than 30 reduces the total
interest paid by $38,000. The online calculator allows you to do
simulations with different amortization periods.

In most cases, however, it is better to exercise caution by opting for a longer period,
which is what Louis-François Éthier recommends. “The shorter the
amortization, the higher the periodic payments. You need to ensure
that your budget allows for this.”

Above all, even if you have chosen a longer term, you can always opt
for accelerated
repayment. “These options go directly to the return of capital and
thus reduce the length of amortization and the interest,” explains
Éthier. “When you have a little extra in your budget, it’s very
beneficial.” You can make an additional payment, make an early
repayment or even increase the amount of your payments. Because
certain restrictions apply, depending on the type of loan, speak with
your advisor to establish the best strategy.

Car loan

You also need to consider amortization when you buy a car with a
loan. If you are looking to pay the lowest payments possible, take
time to do some calculations before you make a decision. The smaller
your payments, the longer your amortization and the more you will pay
in interest.

For example, interest on a car loan of $31,640 at 6.34% over 7 years
would total $7,557. If the loan is amortized over 5 years, the
interest would be $5,299. You would save $2,258 by reducing the loan
term by two years. However, payments would change from $107.34 a week
to $141.50.

You also need to consider depreciation, which is the difference
between the purchase price and the resale price. The moment a car
leaves the dealership, it begins to lose value. A new vehicle loses
half of its value in three years. Depreciation then continues at a
rate of about 8 to 10% per year. Consider this when the time comes to
choose the amortization period. Can you afford to make higher
payments? Opt for a shorter amortization, unless you decide to keep
your vehicle longer. Otherwise, if you amortize your loan over seven
years and you resell your vehicle after 36 months, its resale value
could be lower than the balance of your debt. In the previous example,
the vehicle for which you paid $31,640 will have an estimated value of
$15,820, while the debt would amount to $19,770. Amortized over 5
years, the latter would be $13,866.

Personal loan

“A personal loan helps pay for short-term expenses, such as
renovations, travel or a wedding,” says Éthier. “The amortization
period does not exceed five years.” Because it is not secured by
assets used as collateral, as is the case with a car or mortgage loan,
a personal loan often requires a higher interest rate.

Whether a mortgage loan, person
loan or even a car loan, amortization has a significant impact on
the total interest you will pay. Don’t hesitate to discuss this with
an advisor at your bank to weigh the pros and cons of choosing a
shorter or longer term. Together, you can consider different scenarios.

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